An inverse problem for generalized Kelvin–Voigt equation with p-Laplacian and damping term Full article
| Journal |
Inverse Problems
ISSN: 0266-5611 |
||||||
|---|---|---|---|---|---|---|---|
| Output data | Year: 2021, Volume: 37, Number: 8, Pages: 085012 Pages count : 1 DOI: 10.1088/1361-6420/ac1362 | ||||||
| Tags | Damping term; Existence; Inverse problem; Kelvin–Voigt equations; p-Laplacian; Uniqeness | ||||||
| Authors |
|
||||||
| Affiliations |
|
Abstract:
In this paper, we consider the nonlinear inverse problem for generalized Kelvin-Voigt equations with the p-Laplace diffusion and damping term, describing the motion of incompressible viscous fluids. We assume that the damping term in the momentum equation depends on whether its signal is positive or negative, which may realizes the presence of a source or a sink within the system. The investigated inverse problem consists of finding a coefficient f(t) of the right-hand side of the momentum equation, a vector of velocity field v, and a pressure π. An additional information on a solution of the inverse problem is given as integral overdetermination condition. Under several assumptions on the exponents p, m, the coefficients μ, κ, γ, the dimension of the space d, and specified initial data, we prove the existence and uniqueness of the weak solution of the problem.
Cite:
Antontsev S.N.
, Khompysh K.
An inverse problem for generalized Kelvin–Voigt equation with p-Laplacian and damping term
Inverse Problems. 2021. V.37. N8. P.085012. DOI: 10.1088/1361-6420/ac1362 WOS Scopus РИНЦ OpenAlex
An inverse problem for generalized Kelvin–Voigt equation with p-Laplacian and damping term
Inverse Problems. 2021. V.37. N8. P.085012. DOI: 10.1088/1361-6420/ac1362 WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000678357800001 |
| Scopus: | 2-s2.0-85112663113 |
| Elibrary: | 47021004 |
| OpenAlex: | W3179639452 |